Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void _read(T& x) {
  cin >> x;
}
void R() {}
template <typename T, typename... U>
void R(T& head, U&... tail) {
  _read(head);
  R(tail...);
}
template <typename T>
inline void _write(const T& x) {
  cout << x << ' ';
}
void W() { cout << endl; }
template <typename T, typename... U>
void W(const T& head, const U&... tail) {
  _write(head);
  W(tail...);
}
template <typename T>
void debug(vector<T> V) {
  for (auto x : V) {
    cout << x << " ";
  }
  cout << endl;
}
void go();
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  go();
  return 0;
}
void go() {
  int n;
  R(n);
  vector<pair<int, int> > ans;
  int x = 1, y = 1;
  ans.push_back({x, y});
  for (int i = 2; i <= n; i++) {
    if (i & 1) {
      x++;
    } else {
      y++;
    }
    ans.push_back({x, y});
  }
  W(max(x, y));
  for (auto w : ans) {
    W(w.first, w.second);
  }
}